Homoclinic bifurcations leading to the emergence of bursting oscillations in cell models

摘要: We present a qualitative analysis of generic model structure that can simulate the bursting and spiking dynamics many biological cells. Four different scenarios for emergence are described. In this connection number theorems stated concerning relation between phase portraits fast subsystem global behavior full model. It is emphasized onset involves formation homoclinic orbit travels along route oscillations and, hence, cannot be explained in terms bifurcations subsystem. one scenarios, arise bifurcation which one-dimensional (1D) stable manifold saddle point becomes attracting to its whole 2D unstable manifold. This type bifurcation, complex it produce, have not previously been examined detail. derive flow-defined map situation show how transforms disk-shaped cross-section flow into an annulus. Preliminary investigations produces interesting cascade alternating pitchfork boundary collision bifurcations.